MODIS has multiple detectors per scan. The stripes you are seeing are at the scan boundaries. We do our best to mitigate this calibration artifact, but it will never be completely eliminated. That said it is not as evident when I process the scene. Are you using the latest calibration?
What may work for you may not work for someone else's favorite neck of the kelp forest. In fact, what works for you today, may not work six months from now.
That said, the fixed AOT approach is a decent choice, but as you found even that doesn't resolve all the "problems". Your ROI is pretty close to land, yes geographically, but I mean optically.
You could try using the rhos product, which does not employ an aerosol correction.
Try using 2130 for the cloud_wave and lower the cloud_thresh to 0.018.
The "iterative approach" is described in the Hu paper...it's a manual method.
BTW, FLH is a standard product in our Level-2 Ocean Color data for the MODIS instruments.
Just a follow up question for this comment. When using fixed AOT approach, L2gen need to specify a AOT value for the entire image. Don't know if there is way to use pixel-specific AOT (i.e., a AOT image with several bands instead of a single value)? The aerosol conditions may very over a large area.